Problem 21 - Basic College Mathematics

Question

The following prices per stalk of Brussels sprouts were found at five farmers' markets: $$ \begin{array}{llll} \$ 3.99, & \$ 4.49, & \$ 4.99, & \$ 3.99, & \$ 3.49 . \end{array} $$ What was the mean price per stalk? the median price? the mode?

Step-by-Step Solution

Answer

Mean: \( \$4.19 \), Median: \( \$3.99 \), Mode: \( \$3.99 \).

Step 1 - List the Prices

Record the given prices per stalk of Brussels sprouts: \( \$3.99, \$4.49, \$4.99, \$3.99, \$3.49 \).

Step 2 - Calculate the Mean

Add all the prices together: \( 3.99 + 4.49 + 4.99 + 3.99 + 3.49 = 20.95 \). Now, divide the sum by the number of prices (5): \( \frac{20.95}{5} = 4.19 \). Therefore, the mean price per stalk is \( \$4.19 \).

Step 3 - Arrange the Prices in Ascending Order

Sort the prices in ascending order: \( \$3.49, \$3.99, \$3.99, \$4.49, \$4.99 \).

Step 4 - Identify the Median

The median is the middle value in the arranged list. Since there are 5 prices, the median is the third value: \( \$3.99 \).

Step 5 - Identify the Mode

The mode is the value that appears most frequently. The price \( \$3.99 \) appears twice. Therefore, the mode is \( \$3.99 \).

Key Concepts

mean calculation

The mean gives us the average value of a set of numbers. Let's learn how to calculate it using our given prices per stalk of Brussels sprouts.
First, list all the prices: \(3.99, \)4.49, \(4.99, \)3.99, \(3.49. The formula for the mean is:

\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}.

To calculate the mean:

• Add up all the prices: \)3.99 + \(4.49 + \)4.99 + \(3.99 + \)3.49 = \(20.95.
• Next, divide the sum by the number of prices: \frac{20.95}{5} = 4.19.

So, the mean price per stalk is \)4.19.

median calculation

The median is the middle value in a list of numbers arranged in ascending order. To find the median, follow these steps:
First, sort the prices: \(3.49, \)3.99, \(3.99, \)4.49, \(4.99.
Since there are five prices, the median will be the third price in the sorted list, as there is an odd number of values. The steps are:

• Arrange the prices in ascending order: \)3.49, \(3.99, \)3.99, \(4.49, \)4.99
• Identify the middle value: The third price in the list is \(3.99.
  So, the median price per stalk is \)3.99.

mode calculation

The mode is the value that appears most frequently in a set of numbers. Here's how to find the mode from our list of prices:
Look at the list of prices: \(3.99, \)4.49, \(4.99, \)3.99, \(3.49.
Follow these steps:

• Count the frequency of each price.
• The price \)3.99 appears twice, which is more frequent than any other price in the list.

Therefore, the mode of these prices is $3.99.